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The development of efficient methods for genome-wide association studies (GWAS) between quantitative trait loci (QTL) and genetic values is extremely important to animal and plant breeding programs. Bayesian approaches that aim to select regions of single nucleotide polymorphisms (SNPs) proved to be efficient, indicating genes with important effects. Among the selection criteria for SNPs or regions, selection criterion by percentage of variance can be explained by genomic regions (%var), selection of tag SNPs, and selection based on the window posterior probability of association (WPPA). To also detect potentially associated regions, we proposed measuring posterior probability of the interval PPint), which aims to select regions based on the markers of greatest effects. Therefore, the objective of this work was to evaluate these approaches, in terms of efficiency in selecting and identifying markers or regions located within or close to genes associated with traits. This study also aimed to compare these methodologies with single-marker analyses. To accomplish this, simulated data were used in six scenarios, with SNPs allocated in non?overlapping genomic regions. Considering traits with oligogenic inheritance, WPPA criterion followed by %var and PPint criteria were shown to be superior, presenting higher values of detection power, capturing higher percentages of genetic variance and larger areas. For traits with polygenic inheritance, PPint and WPPA criteria were considered superior. Single?marker analyses identified SNPs associated only in oligogenic inheritance scenarios and was lower than the other criteria. Made available in DSpace on 2022-01-19T15:00:30Z (GMT). No. of bitstreams: 1 evaluation-of-bayesian-methods.pdf: 225633 bytes, checksum: 884b434513d82771927b421541a77455 (MD5) Previous issue date: 2022

The Fisher?s infinitesimal model is traditionally used in quantitative genetics and genomic selection, and it attributes most genetic variance to additive variance. Recently, the dominance maximization model was proposed and it prioritizes the dominance variance based on alternative parameterizations. In this model, the additive effects at the locus level are introduced into the model after the dominance variance is maximized. In this study, the new parameterizations of additive and dominance effects on quantitative genetics and genomic selection were evaluated and compared with the parameterizations traditionally applied using the genomic best linear unbiased prediction method. As the parametric relative magnitude of the additive and dominance effects vary with allelic frequencies of populations, we considered different minor allele frequencies to compare the relative magnitudes. We also proposed and evaluated two indices that combine the additive and dominance variances estimated by both models. The dominance maximization model, along with the two indices, offers alternatives to improve the estimates of additive and dominance variances and their respective proportions and can be successfully used in genetic evaluation. Made available in DSpace on 2022-01-19T16:00:25Z (GMT). No. of bitstreams: 1 evaluation-of-a-new-additive.pdf: 725842 bytes, checksum: 2c26fbbce6a08e566a87f91bb64eca59 (MD5) Previous issue date: 2022

Genomic prediction (GP) offers great opportunities for accelerated genetic gains by optimizing the breeding pipeline. One of the key factors to be considered is how the training populations (TP) are composed in terms of genetic improvement, kinship/origin, and their impacts on GP. Hydrogen cyanide content (HCN) is a determinant trait to guide cassava?s products usage and processing. This work aimed to achieve the following objectives: (i) evaluate the feasibility of using cross-country (CC) GP between germplasm?s of Embrapa Mandioca e Fruticultura (Embrapa, Brazil) and The International Institute of Tropical Agriculture (IITA, Nigeria) for HCN; (ii) provide an assessment of population structure for the joint dataset; (iii) estimate the genetic parameters based on single nucleotide polymorphisms (SNPs) and a haplotype-approach. Datasets of HCN from Embrapa and IITA breeding programs were analyzed, separately and jointly, with 1,230, 590, and 1,820 clones, respectively. After quality control, ~14K SNPs were used for GP. The genomic estimated breeding values (GEBVs) were predicted based on SNP effects from analyses with TP composed of the following: (i) Embrapa genotypic and phenotypic data, (ii) IITA genotypic and phenotypic data, and (iii) the joint datasets. Comparisons on GEBVs' estimation were made considering the hypothetical situation of not having the phenotypic characterization for a set of clones for a certain research institute/country and might need to use the markers? effects that were trained with data from other research institutes/country's germplasm to estimate their clones? GEBV. Fixation index (FST) among the genetic groups identified within the joint dataset ranged from 0.002 to 0.091. The joint dataset provided an improved accuracy (0.8-0.85) compared to the prediction accuracy of either germplasm?s sources individually (0.51-0.67). CC GP proved to have potential use under the present study's scenario, the correlation between GEBVs predicted with TP from Embrapa and IITA was 0.55 for Embrapa's germplasm, whereas for IITA?s it was 0.1. This seems to be among the first attempts to evaluate the CC GP in plants. As such, a lot of useful new information was provided on the subject, which can guide new research on this very important and emerging field. Made available in DSpace on 2022-01-21T16:00:27Z (GMT). No. of bitstreams: 1 can-cross-country.pdf: 5628690 bytes, checksum: b64a514c49f6060f7ee2114524502cc1 (MD5) Previous issue date: 2021

The genotype × environment (G×E) interaction plays an essential role in phenotypic expression and can lead to difficulties in genotypes recommendation. Thus, the objectives of this study were: i) propose the Multi-Environment Index Based on Factor Analysis and Ideotype-Design/Markov Chain Monte Carlo (FAI/MCMC index), and ii) apply it for soybean genotypes recommendation. To this end, a data set with 30 soybean genotypes evaluated in 10 environments for grain yield trait was used. Variance components, genetic parameters and genetic values were estimated through MCMC algorithm. Environmental stratification was conducted by factor analyses and the selection of soybean genotypes was performed using the FAI/MCMC index. The results indicated the existence of genotypic variability and G×E interaction. The environments were grouped into three factors. The predicted genetic gains from indirect selection was 4.81%. Thus, our results suggest that the FAI/MCMC index can be successfully used in soybean breeding. Made available in DSpace on 2022-01-21T01:15:57Z (GMT). No. of bitstreams: 1 environmental-stratification-and-genotype.pdf: 544496 bytes, checksum: 092e3a908598522ee76ed714e37068ca (MD5) Previous issue date: 2021

multicollinearity and high dimensionality problems, making it impossible to obtain stable estimates through the traditional method of estimation based on ordinary least squares. To overcome such challenges, dimensionality reduction methods have been proposed, because of their simple theory and easy application. We compared three dimensionality reduction methods: Principal Components Regression (PCR), Partial Least Squares (PLS), and Independent Components Regression (ICR). An important step for dimensionality reduction and prediction is selecting the number of components, as it affects the linear combinations of the explanatory variables. The linear combinations are inserted into the model to predict the response based on a reduced number of parameters. We examined the criteria for the selection of the number of components. The dimensionality reduction methods were applied to genomic and phenotype data. We evaluated 370 accessions of Asian rice, Oryza sativa, which were genotyped for 36,901 SNPs markers considered to predict the genomic values for the number of panicles per plant trait.This data set presented multicollinearity and high dimensionality. The computational time for each method was also recorded. Among the methods, PCR and ICR gave the highest accuracy values, with ICR standing out for presenting estimates of the least biased genomic values. However, ICR required more computational time than the other methodologies. Made available in DSpace on 2022-01-21T14:30:04Z (GMT). No. of bitstreams: 1 A-comparison-of-regression-methods.pdf: 746875 bytes, checksum: 0a33b4089a790addb685ad71937f7d72 (MD5) Previous issue date: 2021

We aimed to estimate litter size and litter uniformity genetic parameters and genetic trends of Landrace pigs at birth and at three weeks by using multitrait analyses for 2,787 litters. The following litter traits were evaluated: number of piglets born alive (NBA), within-litter weight mean at birth (MBW), within-litter weight standard deviation at birth (SDB), within-litter weight coefficient of variation at birth (CVB), number of piglets at three weeks (NT), within-litter weight mean at three weeks (MT), within-litter weight standard deviation at three weeks (SDT), and within-litter weight coefficient of variation at three weeks (CVT). Heritability estimates for NBA, MBW, SDB, and CVB were 0.09±0.04, 0.31±0.08, 0.01±0.04, and 0.07±0.05, respectively, greater than those obtained at three weeks (0.06±0.04, 0.10±0.06, 0.01±0.04, and 0.02±0.04 for NT, MT, SDT, and CVT, respectively). The genetic correlations between NBA and MBW and between MBW and CVB (−0.73±0.20 and −0.93±0.21, respectively) were of moderate to high magnitudes, as well as the genetic correlations between CVT and SDT (0.85±0.39). Genetic correlations between MBW and MT, SDB and SDT, CVB and CVT, and NBA and NT were 0.73±0.16, 0.69±0.54, 0.36±0.80, and 0.95±0.06, respectively. The genetic trends were linear for NBA and CVB and quadratic for MBW and SDB, whereas for all traits at three weeks, they were close to zero. Within-litter weight coefficient of variation (CV) may be the most appropriate variation measure for application in breeding programs, especially at birth, due to its greater heritability estimate and high and negative genetic correlation with MBW. The genetic trends show that NT does not follow the increase in NBA, emphasizing the need to review the breeding goals.

An accurate, efficient and informative statistical method for analyses of genotype × environment (G × E) interactions is a key requirement for progress in any breeding program. Thus, the objective of this study was to quantify individual variation in reaction norms using random regression models fitted through Legendre polynomials in eucalyptus (Eucalyptus spp.) breeding. To this end, a data set with 215 eucalyptus clones of different species and hybrids evaluated in four environments for diameter at breast height (DBH) and Pilodyn penetration (PP) was used. Variance components were estimated by restricted maximum likelihood, and genetic values were predicted by best linear unbiased prediction. The best-fitted model for DBH and PP was indicated by the Akaike information criterion, and the significance of the genotype effects was tested using the likelihood ratio test. Genetic variability between eucalyptus clones and very high accuracies ( r^gg >=0.90 ) were detected for both traits. Reaction norms and eigenfunctions generated genetic insights into G × E interactions. This is the first study that quantified individual variation in reaction norms using random regression models fitted through Legendre polynomials in eucalyptus breeding and demonstrated the great potential of this technique. Made available in DSpace on 2021-01-29T00:53:54Z (GMT). No. of bitstreams: 1 Quantifying-individual-variation.pdf: 1478774 bytes, checksum: 4b77df5cb6b88900cdea7d542af2e935 (MD5) Previous issue date: 2020

Pedigree information is incomplete by nature and commonly not well-established because many of the genetic ties are not known a priori or can be wrong. The genomic era brought new opportunities to assess relationships between individuals. However, when pedigree and genomic information are used simultaneously, which is the case of single-step genomic BLUP (ssGBLUP), defining the genetic base is still a challenge. One alternative to overcome this challenge is to use metafounders, which are pseudo-individuals that describe the genetic relationship between the base population individuals. The purpose of this study was to evaluate the impact of metafounders on the estimation of breeding values for tick resistance under ssGBLUP for a multibreed population composed by Hereford, Braford, and Zebu animals. Three different scenarios were studied: pedigree-based model (BLUP), ssGBLUP, and ssGBLUP with metafounders (ssGBLUPm). In ssGBLUPm, a total of four different metafounders based on breed of origin (i.e., Hereford, Braford, Zebu, and unknown) were included for the animals with missing parents. The relationship coefficient between metafounders was in average 0.54 (ranging from 0.34 to 0.96) suggesting an overlap between ancestor populations. The estimates of metafounder relationships indicate that Hereford and Zebu breeds have a possible common ancestral relationship. Inbreeding coefficients calculated following the metafounder approach had less negative values, suggesting that ancestral populations were large enough and that gametes inherited from the historical population were not identical. Variance components were estimated based on ssGBLUPm, ssGBLUP, and BLUP, but the values from ssGBLUPm were scaled to provide a fair comparison with estimates from the other two models. In general, additive, residual, and phenotypic variance components in the Hereford population were smaller than in Braford across different models. The addition of genomic information increased heritability for Hereford, possibly because of improved genetic relationships. As expected, genomic models had greater predictive ability, with an additional gain for ssGBLUPm over ssGBLUP. The increase in predictive ability was greater for Herefords. Our results show the potential of using metafounders to increase accuracy of GEBV, and therefore, the rate of genetic gain in beef cattle populations with partial levels of missing pedigree information. Keywords: unknown parent group, founder, genomic selection, missing pedigree, breeding values Made available in DSpace on 2020-12-08T09:05:22Z (GMT). No. of bitstreams: 1 fgene.pdf: 750695 bytes, checksum: feed0a2c3f357eed6e731aa7bc936a64 (MD5) Previous issue date: 2020 Article 556399.

Cassava improvement using traditional breeding strategies is slow due to the species? long breeding cycle. However, the use of genomic selection can lead to a shorter breeding cycle. This study aimed to estimate genetic parameters for productive traits based on pedigree (pedigree and phenotypic information) and genomic (markers and phenotypic information) analyses using biparental crosses at different stages of selection. A total of 290 clones were genotyped and phenotyped for fresh root yield (FRY), dry matter content (DMC), dry yield (DY), fresh shoot yield (FSY) and harvest index (HI). The clones were evaluated in clonal evaluation trials (CET), preliminary yield trials (PYT), advanced yield trials (AYT) and uniform yield trials (UYT), from 2013 to 2018 in ten locations. The breeding stages were analyzed as follows: one stage (CET), two stages (CET and PYT), three stages (CET, PYT and AYT) and four stages (CET, PYT, AYT and UYT). The genomic predictions were analyzed via k-fold cross-validation based on the genomic best linear unbiased prediction (GBLUP) considering a model with genetic additive effects and genotype × location interactions. Genomic and pedigree accuracies were moderate to high (0.56?0.72 and 0.62?0.78, respectively) for important starch-related traits such as DY and FRY; when considering one breeding stage (CET) with the aim of early selection, the genomic accuracies ranged from 0.60 (DMC) to 0.71 (HI). Moreover, the correlations between the genomic estimation breeding values of one-stage genomic analysis and the estimated breeding values of the four-stage (full data set) pedigree analysis were high for all traits as well as for a selection index including all traits. The results indicate great possibilities for genomic selection in cassava, especially for selection early in the breeding cycle (saving time and effort). Made available in DSpace on 2019-11-08T18:17:13Z (GMT). No. of bitstreams: 1 2019M.DeonPOGenomic.pdf: 1434791 bytes, checksum: ac270d3dcac3dc8030251746a09207b5 (MD5) Previous issue date: 2019

A cultura do arroz tem grande importância nacional e mundial por ser um dos cereais mais produzidos e consumidos no mundo, caracterizando-se como o principal alimento de mais da metade da população mundial. Em função de sua importância alimentar, desenvolver métodos eficientes que visam a predição e a seleção de indivíduos geneticamente superiores, quanto a características da planta, é de extrema importância para os programas de melhoramento. Diante disso, o objetivo deste trabalho foi avaliar e comparar a eficiência do método Delta-p, G-BLUP, BayesCpi, BLASSO e o índice Delta-p/G-BLUP, índice Delta-p/BayesCpi e índice Delta-p/BLASSO, na estimação de valores genômicos e dos efeitos de marcadores SNPs (Single Nucleotide Polymorphisms) em dados fenotípicos associados a características de arroz. A utilização de marcadores moleculares permite alta eficiência seletiva e o aumento do ganho genético por unidade de tempo. O método Delta-p utiliza o conceito de mudança na frequência alélica devido à seleção e o conceito teórico de ganho genético. O Índice é baseado no princípio da seleção combinada, utiliza conjuntamente as informações dos valores genômicos aditivos preditos via G-BLUP, BayesCpi ou BLASSO e via Delta-p. Estes métodos foram aplicados e comparados quanto à predição genômica utilizando nove características de arroz (Oryza sativa), sendo elas: comprimento da folha bandeira, largura da folha bandeira; número de panículas por planta; número de ramos da panícula primária; comprimento de semente; largura de semente; teor de amilose; teor de proteína; resistência a bruzone. O índice Delta-p/G-BLUP obteve maiores capacidades preditivas para as características estudadas, exceto para a característica Conteúdo de amilose, em que o método que obteve maior capacidade preditiva foi o BayesCpi, sendo aproximadamente 3% superior ao índice Delta-p/G-BLUP. Made available in DSpace on 2019-07-27T00:52:09Z (GMT). No. of bitstreams: 1 2019M.DeonCRCombined.pdf: 1296470 bytes, checksum: 227d888221e1f80c35124794b6813cff (MD5) Previous issue date: 2019

The availability of high-density molecular markers in common bean has allowed to explore the genetic basis of important complex agronomic traits with increased resolution. Genome-Wide Association Studies (GWAS) and Regional Heritability Mapping (RHM) are two analytical approaches for the detection of genetic variants. We carried out GWAS and RHM for plant architecture, lodging and productivity across two important growing environments in Brazil in a germplasm of 188 common bean varieties using DArTseq genotyping strategies. The coefficient of determination of G · E interaction (c2 int) was equal to 17, 21 and 41%, respectively for the traits architecture, lodging, and productivity. Trait heritabilities were estimated at 0.81 (architecture), 0.79 (lodging) and 0.43 (productivity), and total genomic heritability accounted for large proportions (72% to 100%) of trait heritability. At the same probability threshold, three marker?trait associations were detected using GWAS, while RHM detected eight QTL encompassing 145 markers along five chromosomes. The proportion of genomic heritability explained by RHM was considerably higher (35.48 to 58.02) than that explained by GWAS (28.39 to 30.37). In general, RHM accounted for larger fractions of the additive genetic variance being captured by markers effects inside the defined regions. Nevertheless, a considerable proportion of the heritability is still missing (42% to 64%), probably due to LD between markers and genes and/or rare allele variants not sampled. RHM in autogamous species had the potential to identify larger-effect QTL combining allelic variants that could be effectively incorporated into whole-genome prediction models and tracked through breeding generations using marker-assisted selection. Made available in DSpace on 2018-09-18T00:41:40Z (GMT). No. of bitstreams: 1 2018M.DeonG3Genomewide.pdf: 1476838 bytes, checksum: ad2596aa80cc16027d13266642284b81 (MD5) Previous issue date: 2018-09-17

EnglishWe aimed to apply genomic information based on SNP (single nucleotide polymorphism) markers for the genetic evaluation of the traits “stay-green” (SG), plant architecture (PA), grain aspect (GA) and grain yield (GY) in common bean through Bayesian models. These models were compared in terms of prediction accuracy and ability for heritability estimation for each one of the mentioned traits. A total of 80 cultivars were genotyped for 377 SNP markers, whose effects were estimated by five different Bayesian models: Bayes A (BA), B (BB), C (BC), LASSO (BL) e Ridge regression (BRR). Although, prediction accuracies calculated by means of cross-validation have been similar within each trait, the BB model stood out for the trait SG, whereas the BRR was indicated for the remaining traits. The heritability estimates for the traits SG, PA, GA and GY were 0.61, 0.28, 0.32 and 0.29, respectively. In summary, the Bayesian methods applied here were effective and ease to be implemented. The used SNP markers can help in the early selection of promising genotypes, since incorporating genomic information increase the prediction accuracy of the estimated genetic merit. Key words: Phaseolus vulgaris; SNP markers; cross-validation portuguesObjetivou-se incorporar informacoes genomicas de marcadores SNP (“single nucleotide polymorphism”) na avaliacao genetica das caracteristicas “stay-green” (SG), arquitetura de planta (AP), aspecto de graos (AG) e produtividade de graos (PG) em feijoeiro-comum via modelos Bayesianos. Estes modelos foram comparados quanto a acuracia de predicao e habilidade de estimacao da herdabilidade para cada caracteristica. Utilizaram-se informacoes de 80 cultivares genotipadas para 377 marcadores SNP, cujos efeitos de substituicao alelica foram estimados por meio de cinco diferentes modelos Bayesianos: Bayes A (BA), B (BB), C (BC), LASSO (BL) e regressao “ridge” (BRR). Embora as acuracias de predicao calculadas por meio de analise de validacao cruzada tenham sido similares dentro de cada caracteristica, o modelo BB se destacou para a caracteristica SG, enquanto o modelo BRR foi indicado para as demais. As herdabilidades estimadas para SG, AP, AG e PG foram, respectivamente, 0,61, 0,28, 0,32 e 0,29. Em resumo, os metodos contemplados mostraram-se efetivos e de facil implementacao. O conjunto de marcadores utilizado pode auxiliar na selecao precoce de genotipos promissores, uma vez que a incorporacao de informacoes genomicas aumenta a acuracia de predicao do merito genetico estimado. Palavras-chave: Phaseolus vulgaris; marcadores SNP; validacao cruzada

We proposed a population structure correction for genome-wide selection based on covariance analysis via eigenvector (EVG) decomposition. The agreement between the predicted and true breeding values was evaluated by independent cross-validation data sets. Other correction methods such as correction via principal components, best linear unbiased prediction, and deregressed phenotype were also evaluated. Based on different simulation scenarios, the proposed EVG out performed the other methods in the prediction of accuracy. Made available in DSpace on 2018-01-02T23:18:58Z (GMT). No. of bitstreams: 1 2017M.DeonCBABPopulation.pdf: 487075 bytes, checksum: 0a6cf1d2c331d3b73c1a5b9cbc45272c (MD5) Previous issue date: 2018-01-02

Em seleção genômica (SG), o grande número de marcadores moleculares utilizados, bem como a demanda computacional dos modelos bayesianos, fundamentados nos algoritmos Monte Carlo Via Cadeias de Markov, faz com que as análises exijam semanas ou até meses de processamento. A computação paralela representa uma solução natural para este problema, visto que esta subdividi um algoritmo em várias tarefas independentes, as quais podem ser processadas em paralelo, reduzindo o tempo de processamento. Objetivou-se comparar a eficiência de processamento do método BayesCπ programado em paralelo com o seu algoritmo sequencial padrão. Duas estratégias de paralelização foram estudadas. A primeira envolveu a análise de múltiplas cadeias MCMC em paralelo, e a segunda referiu-se à paralelização de uma única cadeia MCMC. Utilizou-se a biblioteca MPI e o pacote OpenMPI associado ao compilador gfortran para execução em paralelo desses algoritmos. Foram utilizados dados simulados considerando 10.000 marcadores SNPs e 4.100 indivíduos. O algoritmo sequencial padrão foi processado em 77,29 horas. Ao usar múltiplas cadeias em paralelo o processamento foi 77% mais rápido (17,75hs), enquanto que a estratégia de paralelização de uma única cadeia apresentou um ganho de desempenho de 15% (65,37hs). Conclui-se que a computação paralela é eficiente e pode ser aplicada à SG. Made available in DSpace on 2018-01-03T23:20:01Z (GMT). No. of bitstreams: 1 2017M.DeonRBMComputacao.pdf: 3436591 bytes, checksum: ce6c6c3a2cd1f8314a1acc84ae2d7af4 (MD5) Previous issue date: 2018-01-03

Recentemente, efeitos de dominância, têm sido incluídos na seleção genômica de várias espécies, sendo o método GBLUP-D o mais utilizado. Esse método consiste em substituir, no procedimento REML/BLUP, as matrizes de parentesco baseadas no pedigree pelas matrizes com base nos marcadores moleculares. Este método pode ser realizado por meio do software GVCBLUP ou por meio do pacote BGLR do software R, o qual se baseia em regressão bayesiana via Kernel de Reprodução do Espaço de Hilbert. Objetivou-se nesse trabalho avaliar a possibilidade e efetividade de implementação do GBLUP-D via a função lmekin implementada no pacote coxme do software R por meio da inclusão das matrizes de parentesco genômicos aditivo e de dominância. Assim, comparou-se, via análises de dados simulados, os resultados obtidos pela função lmekin com os obtidos pelo software GVCBLUP e pacote BGLR. Os resultados mostraram que os métodos GBLUP e GBLUP-D ajustados via REML no software GVCBLUP e por meio da função lmekin são equivalentes. Assim, a função lmekin é uma alternativa eficiente para o ajuste, no software R, de modelos genômicos contemplando efeitos aditivos e de dominância. Made available in DSpace on 2018-01-03T23:19:49Z (GMT). No. of bitstreams: 1 2017M.DeonRBMProposta.pdf: 485345 bytes, checksum: a69b87e91a75fc149e384de296da0d9c (MD5) Previous issue date: 2018-01-03

O objetivo deste trabalho foi propor uma abordagem bayesiana do método de Eberhart & Russell para avaliar a adaptabilidade e da estabilidade fenotípica de genótipos de alfafa (Medicago sativa), bem como avaliar a eficiência da utilização de distribuições a priori informativas e pouco informativas. Foram utilizados dados de um experimento em blocos ao acaso, no qual se avaliou a produção de massa de matéria seca de 92 genótipos. A metodologia bayesiana proposta foi implementada no programa livre R por meio da função MCMCregress do pacote MCMCpack. Para representar as distribuições a priori pouco informativas, utilizaram-se distribuições de probabilidade com grande variância; e, para representar distribuições a priori informativas, adotou-se o conceito de meta-análise, que se caracteriza pela utilização de informações provenientes de trabalhos anteriores. A comparação entre as distribuições a priori foi realizada por meio do fator de Bayes, com a função BayesFactor do pacote MCMCpack, que indicou a priori informativa como a mais adequada nas condições deste estudo. The objective of this work was to propose a Bayesian approach for the Eberhart & Russell method to evaluate the phenotypic adaptability and stability of alfafa (Medicago sativa) genotypes, as well as to evaluate the efficiency of the use of prior informative and noninformative distributions. Data from a randomized block design experiment evaluating the forage dry weight of 92 genotypes were used. The Bayesian methodology proposed was implemented in the free software R by the MCMCregress function of the MCMCpack package. To represent the noninformative prior distributions, a probability distribution with high variance was used; and, to represent the informative prior, a meta-analysis concept was adopted, characterized by the use of information provided by previous studies. The comparison between the prior distributions was done using the Bayes Factor, with the BayesFactor function of the MCMCpack package, which indicated that an informative prior is more appropriate under the conditions of this study.

This study aimed at investigating the genetic divergence of eighteen accessions of cupuaçu trees based on fruit morphometric traits and comparing usual methods of cluster analysis with the proposed multiscale bootstrap resampling methodology. The data were obtained from an experiment conducted in Tomé-Açu city (PA, Brazil), arranged in a completely randomized design with eighteen cupuaçu accessions and 10 repetitions, from 2004 to 2011. Genetic parameters were estimated by restricted maximum likelihood/best linear unbiased prediction (REML/BLUP) methodology. The predicted breeding values were used in the study on genetic divergence through Unweighted Pair Cluster Method with Arithmetic Mean (UPGMA) hierarchical clustering and Tocher’s optimization method based on standardized Euclidean distance. Clustering consistency and optimal number of clusters in the UPGMA method were verified by the cophenetic correlation coefficient (CCC) and Mojena’s criterion, respectively, besides the multiscale bootstrap resampling technique. The use of the clustering UPGMA method in situations with and without multiscale bootstrap resulted in four and five clusters, respectively, while the Tocher’s method resulted in seven clusters. The multiscale bootstrap resampling technique proves to be efficient to assess the consistency of clustering in hierarchical methods and, consequently, the optimal number of clusters.